On qq-deformed generalized Touchard polynomials

A qq-deformed analog of the generalized Touchard polynomials is considered and the connection to generalized Stirling numbers and Bell polynomials is established. For low order mm, the qq-deformed generalized Touchard polynomials are shown to be related to qq-deformed exponential polynomials (m=1m=1), qq-deformed Laguerre polynomials (m=2m=2), and qq-deformed Bessel polynomials (m=−1m=−1). A recurrence relation for the qq-deformed generalized Touchard polynomials is derived, representing a generalization of Spivey’s relation.